Question

the table shows the conversion of several amounts of liters to liquid pints.
liters (x) | liquid pints (y)
5 | 10.55
7 | 14.77
9 | 18.99
11 | 23.21
which equation represents the relationship between the number of liters, x, and the number of liquid pints, y?
○ $y = x + 5.55$
○ $y = x - 5.55$
○ $y = 2.11x$
○ $y = \frac{x}{2.11}$

Explanation:

Step1: Check first option

Substitute \( x = 5 \) into \( y = x + 5.55 \). We get \( y = 5 + 5.55 = 10.55 \), which matches the first pair. Now check \( x = 7 \): \( y = 7 + 5.55 = 12.55 \), but the table has \( y = 14.77 \). So first option is wrong.

Step2: Check second option

Substitute \( x = 5 \) into \( y = x - 5.55 \). We get \( y = 5 - 5.55 = - 0.55 \), which does not match \( y = 10.55 \). So second option is wrong.

Step3: Check third option

Substitute \( x = 5 \) into \( y = 2.11x \). We get \( y = 2.11\times5 = 10.55 \), which matches. Check \( x = 7 \): \( y = 2.11\times7 = 14.77 \), which matches. Check \( x = 9 \): \( y = 2.11\times9 = 18.99 \), which matches. Check \( x = 11 \): \( y = 2.11\times11 = 23.21 \), which matches.

Step4: Check fourth option

Substitute \( x = 5 \) into \( y=\frac{x}{2.11}\). We get \( y=\frac{5}{2.11}\approx2.37 \), which does not match \( y = 10.55 \). So fourth option is wrong.

Answer:

\( y = 2.11x \) (the third option)